This is an impactful yet controversial scene that baffles even the Japanese viewers. In chapter 22 of the original, semi-autobiographical manga that the Ghibli film is based on, the author speculates that Taeko's father physically punished Taeko because she was not acting in line with his principle of raising a dignified (read of higher class) daughter. This is because in post-war Japan, including the time of Taeko's childhood in 1966, barefootedness (outside of house) was commonly associated with poverty. (Cf. the classic manga Barefoot Gen by Hiroshima survivor Keiji Nakazawa that is also a testimony to the living conditions of the impoverished people.) Whether Taeko was acting selfish or bratty probably was of no concern to her father.
原作コミック（岡本蛍・作 刀根夕子・画）の２２話「ワガママ」には
「ひょっとして父は・・・タエ子のワガママにいまさら腹を立てたのではなかったかもしれないはだしで飛び出すというそのみっともなさ あさましさに激怒したのではなかったろうか ワガママでもいい 凛々しく育ってほしい・・・それが父の美学だったのかもしれない」
Quoted from http://detail.chiebukuro.yahoo.co.jp/qa/question_detail/q13117211068.
On a side note, はだし教育 (hadashi kyouiku, Barefoot Education) is generally well-received these days, so I don't think that children leaving the house without shoes on would incur that kind of penalty anymore.
Inspired by a post-viewing reflection article (in Japanese, a good read), I think the scene of Taeko running out of the house in barefoot prompted the recall of the original inferiority feeling by the father and was treated as an attack on his feeling of superiority that was his defense mechanism. It is all based on assumptions really, but could it be that the father was once poor and worked his way up to the middle-upper class? Was his sumptuous lifestyle (e.g. buying the then rare and expensive pineapple and not finish eating it) an overcompensation for his earlier days? The relevant parts in the Wikipedia articles (emphasis by me):
Superiority complex is a psychological defense mechanism in which a person's feelings of superiority counter or conceal his or her feelings of inferiority. [...] [I]f we inquire into a superiority complex and study its continuity, we can always find a more or less hidden inferiority [feeling] complex.
[Inferiority complex] is often subconscious, and is thought to drive afflicted individuals to overcompensate, resulting either in spectacular achievement or extreme asocial behavior. [...] A secondary inferiority feeling relates to an adult's experience of being unable to reach a subconscious, fictional final goal of subjective security and success to compensate for the inferiority feelings. The perceived distance from that goal would lead to a negative/depressed feeling that could then prompt the recall of the original inferiority feeling; this composite of inferiority feelings could be experienced as overwhelming.
The inner workings of human beings are really complex, as this example in the film has shown, with many viewers, myself included, still begging for an explanation of the motives behind the father's action. There may never be a definitive answer.
